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A new method for the design of hybrid position/force controllers for constrained manipulators is derived. This method can be applied to all types of constraint due to contact with the environmcnt; including constraint due to contact at the end effector, constraint due to more than one robot manipulating a workpiece, and constraint due to the bracing of a robot arm against a work surface. The manipulator and its contact with the environment are modeled in terms of lower order pairs. From this model a general equation describing the constraint on the motion of the arm is derived. The task is modeled as a set of essential position vectors and a set of essential force vectors. A hybrid position/force controller is derived to control the position and force at the joints of a manipulator such that the motion of the the robot conforms to the constraints imposed on it due to contact with the environment; and the motion at the end effector, and the force at the contact with the environment are those required for the performance of the task. The method is illustrated by a simple three degree of freedom example.